Big numbers

what's the biggest number you can write in 15 seconds?

9 > 1
99 > 9
99+99 > 99
99*99 > 99+99
99⁹⁹ > 99*99
99⁹⁹⁹⁹ > 99⁹⁹

this is where it gets more interesting.

2 ↑ 2 = 2² = 4
3 ↑ 3 = 3³³ = 19683
3 ↑ 4 = 3³³³ = lots

3 (↑²) 3 = (3↑3) ↑ (3↑3) = 19683 ↑ 19683

so where: f(n) = n ↑ⁿ n
and f³(n) = f(f(f(n)))

my big number is: fⁿ(n) where n = 9

mr. xkcd would have beaten me though with BB(9). he could have had BB⁹(9 ↑⁹ 9) but it would, frankly, have been unnecessary wear and tear on his pencil. in other words, it would have reduced the computational density.

actually he goes bigger. he also restates the problem in a more exact form, 32 characters instead of 15 seconds. and btw, yes this entire discussion was sparked/ripped by/from his post and my vague recollections of a conversation with josh.